An Introduction To Ordinary Differential Equations

An Introduction to Ordinary Differential Equations PDF
Get This Book
Author: Earl A. Coddington
Publisher: Courier Corporation
ISBN: 9780486659428
Size: 73.72 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 292
View: 1480

A thorough and systematic first course in elementary differential equations for undergraduates in mathematics and science, with many exercises and problems (with answers).


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: Wolfgang Walter
Publisher: Springer Science & Business Media
ISBN: 1461206014
Size: 27.91 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 384
View: 2490

Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: Morris Tenenbaum
Publisher: Courier Corporation
ISBN: 0486649407
Size: 25.99 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 808
View: 2554

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: Hartmut Logemann
Publisher: Springer
ISBN: 9781447163978
Size: 53.55 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 333
View: 7269

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions, • continuous dependence on initial data, • flows, • qualitative behaviour of solutions, • limit sets, • stability theory, • invariance principles, • introductory control theory, • feedback and stabilization. The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability. Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: L. S. Pontryagin
Publisher: Elsevier
ISBN: 1483156494
Size: 75.75 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 304
View: 5318

Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: Edward L. Ince
Publisher: Courier Corporation
ISBN: 0486603490
Size: 50.32 MB
Format: PDF, Mobi
Category : Mathematics
Languages : un
Pages : 558
View: 3655

Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; further developments in the theory of boundary problems; existence theorems, equations of first order; nonlinear equations of higher order; more. "Highly recommended" — Electronics Industries.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: Bhamra
Publisher: Allied Publishers
ISBN: 9788177644890
Size: 26.37 MB
Format: PDF, Docs
Category :
Languages : un
Pages :
View: 7345



Ordinary Differential Equations And Dynamical Systems

Ordinary Differential Equations and Dynamical Systems PDF
Get This Book
Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821883283
Size: 51.59 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : un
Pages : 356
View: 1553

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.


Ordinary Differential Equations

Ordinary Differential Equations PDF
Get This Book
Author: D. Somasundaram
Publisher: CRC Press
ISBN: 9780849309885
Size: 64.67 MB
Format: PDF, Kindle
Category : Mathematics
Languages : un
Pages : 295
View: 2971

Though ordinary differential equations is taught as a core course to students in mathematics and applied mathematics, detailed coverage of the topics with sufficient examples is unique. Written by a mathematics professor and intended as a textbook for third- and fourth-year undergraduates, the five chapters of this publication give a precise account of higher order differential equations, power series solutions, special functions, existence and uniqueness of solutions, and systems of linear equations. Relevant motivation for different concepts in each chapter and discussion of theory and problems-without the omission of steps-sets Ordinary Differential Equations: A First Course apart from other texts on ODEs. Full of distinguishing examples and containing exercises at the end of each chapter, this lucid course book will promote self-study among students.


Ordinary Differential Equations Basics And Beyond

Ordinary Differential Equations  Basics and Beyond PDF
Get This Book
Author: David G. Schaeffer
Publisher: Springer
ISBN: 1493963899
Size: 72.39 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 542
View: 7409

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).